Learning Analysis
Adani B. Abutto
2025-06-06
1 Data Import and Cleaning
1.1 Stimuli
# import stimuli information
df.stimuli =
read_csv(paste0(stim_dir,
"fun-puzzles-exp1/production2_puzzles-test.csv"))
df.stimuli %>%
head()## # A tibble: 6 × 15
## puzzle_id collection_name level_name layout level_width level_height
## <dbl> <chr> <dbl> <chr> <dbl> <dbl>
## 1 0 Microban 67 ['###… 7 8
## 2 1 Microban 33 ['###… 7 7
## 3 2 Microban 26 [' ##… 6 8
## 4 3 Sokogen-990602… 13 ['###… 8 6
## 5 4 Sokogen-990602… 19 ['###… 6 6
## 6 5 Sokogen-990602… 41 ['###… 9 7
## # ℹ 9 more variables: sokobanonline__likes_rate <dbl>,
## # sokobanonline__solve_rate <dbl>,
## # sokobanonline__shortest_solution <dbl>, enjoyment_cat <chr>,
## # difficulty_cat <chr>, shortestPath_cat <chr>, stimuli_set <chr>,
## # boxes <chr>, start_position <chr>1.2 Metadata
## # A tibble: 6 × 20
## puzzle_id collection_name level_name layout level_width level_height
## <dbl> <chr> <dbl> <chr> <dbl> <dbl>
## 1 0 Microban 67 ['###… 7 8
## 2 1 Microban 33 ['###… 7 7
## 3 2 Microban 26 [' ##… 6 8
## 4 3 Sokogen-990602… 13 ['###… 8 6
## 5 4 Sokogen-990602… 19 ['###… 6 6
## 6 5 Sokogen-990602… 41 ['###… 9 7
## # ℹ 14 more variables: sokobanonline__likes_rate <dbl>,
## # sokobanonline__solve_rate <dbl>,
## # sokobanonline__shortest_solution <dbl>, enjoyment_cat <chr>,
## # difficulty_cat <chr>, shortestpath_cat <chr>, stimuli_set <chr>,
## # boxes <chr>, start_position <chr>, shortest_solution <dbl>,
## # astar_solution <chr>, astar_iters <dbl>,
## # astar_solution_length <dbl>, astar_solution_string <chr>1.3 Exclusions
df.exclusions =
read_csv(paste0(data_dir,
"fun-puzzles-exp1/production2_exclusions.csv"))
df.exclusions %>%
count(reasons)## # A tibble: 10 × 2
## reasons n
## <chr> <int>
## 1 Failed comprehension 2
## 2 Only 1 practice trials 1
## 3 Only 2 practice trials 5
## 4 bad trace log 38
## 5 comparison: only 7 posttest trials 2
## 6 comparison: only 7 pretest trials 4
## 7 empty trace log 12
## 8 test attempts: only 7 trials with trace data 6
## 9 test ratings: only 6 trials 1
## 10 test ratings: only 7 trials 151.4 Exit Survey Data
df.survey =
read_csv(paste0(data_dir,
"fun-puzzles-exp1/production2_survey.csv"))
df.survey_processed =
df.survey %>%
# mutate scales to show labels
mutate(judgedDifficulty = factor(judgedDifficulty,
levels = c(1, 2, 3, 4, 5),
labels = c("1\nVery Easy", "2", "3", "4", "5\nVery Hard")),
participantEffort = factor(participantEffort,
levels = c(1, 2, 3, 4, 5),
labels = c("1\nVery Low", "2", "3", "4", "5\nVery High")),
sokobanFamiliarity = factor(sokobanFamiliarity,
levels = c(0, 1, 2, 3),
labels = c("Never", "A few times", "Several times", "Very familiar")),
gamingFrequency = factor(gamingFrequency,
levels = c(0, 1, 2, 3, 4),
labels = c("None", "< 1h", "1-5h", "6-10h", "> 10h"))) %>%
# filter out exclusions
filter(!gameID %in% df.exclusions$gameID)
df.survey_processed %>%
head()## # A tibble: 6 × 27
## project experiment iteration stim_id gameID condition
## <chr> <chr> <chr> <chr> <chr> <chr>
## 1 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 3940-… difficult
## 2 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 7209-… difficult
## 3 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 4733-… difficult
## 4 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 6110-… difficult
## 5 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 0047-… difficult
## 6 fun-puzzles fun-puzzles-exp1 production2 6790956f9… 2839-… difficult
## # ℹ 21 more variables: startInstructionTS <dbl>,
## # startPracticeTS <dbl>, startPreTS <dbl>, startMainTS <dbl>,
## # startPostTS <dbl>, startSurveyTS <dbl>,
## # startComprehensionTS <dbl>, endExperimentTS <dbl>,
## # participantExplanations <chr>, judgedDifficulty <fct>,
## # participantEffort <fct>, sokobanFamiliarity <fct>,
## # gamingFrequency <fct>, participantYears <dbl>, …1.5 Gameplay Data
8 test trials:
df.game =
read_csv(paste0(data_dir,
"/fun-puzzles-exp1/production2_testTrials.csv"))
df.game_processed =
df.game %>%
# filter out exclusions
filter(!gameID %in% df.exclusions$gameID) %>%
# complement puzzle ids
mutate(puzzle_id = paste(str_sub(collection_name, 1, 7), level_name)) %>%
# rename cols
rename(rating = rate_response,
ratingRT = rate_rt)
df.game_processed %>%
head()## # A tibble: 6 × 32
## project experiment iteration stim_id gameID condition study_phase
## <chr> <chr> <chr> <chr> <chr> <chr> <chr>
## 1 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 2 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 3 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 4 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 5 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## 6 fun-puzzl… fun-puzzl… producti… 679095… 3940-… difficult test
## # ℹ 25 more variables: trialNum <dbl>, stimuli_set <chr>,
## # author_name <chr>, collection_name <chr>, level_name <dbl>,
## # width <dbl>, height <dbl>, layout <chr>, boxes <chr>,
## # start_position.x <dbl>, start_position.y <dbl>,
## # select_response <dbl>, select_rt <dbl>, rating <dbl>,
## # ratingRT <dbl>, solveDuration <dbl>, solved <dbl>,
## # boxesSolved <dbl>, attempt_nInputEvents <dbl>, …# calculate summary ratings
df.summary_ratings =
df.game_processed %>%
# bootstrap ci
group_by(stimuli_set, puzzle_id, condition) %>%
tidyboot_mean(rating, na.rm = T) %>%
ungroup() %>%
# median, sd, etc.
left_join(summarizer(df.game_processed, target_cols = c(rating),
puzzle_id, condition) %>%
dplyr::select(-ends_with('mean')),
by = c("puzzle_id", "condition")) %>%
rename(rating_meanBoot = empirical_stat,
rating_mean = mean,
rating_ciLo = ci_lower,
rating_ciHi = ci_upper)
df.summary_ratings %>%
head()## # A tibble: 6 × 10
## stimuli_set puzzle_id condition n rating_meanBoot rating_ciLo
## <chr> <chr> <chr> <int> <dbl> <dbl>
## 1 A Microba 104 difficult 36 9.08 8.51
## 2 A Microba 104 enjoyable 32 4.28 3.41
## 3 A Microba 67 difficult 36 8.67 8
## 4 A Microba 67 enjoyable 32 4.03 3.23
## 5 A Sokogen 13 difficult 36 7.25 6.29
## 6 A Sokogen 13 enjoyable 32 5.59 4.57
## # ℹ 4 more variables: rating_mean <dbl>, rating_ciHi <dbl>,
## # rating_median <dbl>, rating_sd <dbl># add avg ratings to game data df
df.game_processed =
df.game_processed %>%
left_join(df.summary_ratings %>%
dplyr::select(condition, puzzle_id, rating_mean) %>%
pivot_wider(names_from = condition, values_from = rating_mean)) %>%
rename(mean_difficult = difficult,
mean_enjoyable = enjoyable) %>%
mutate(puzzle_id_sorted = reorder(puzzle_id, mean_difficult))16 comparison trials:
df.comparison =
read_csv(paste0(data_dir,
"fun-puzzles-exp1/production2_compareTrials.csv"))
df.comparison_processed =
df.comparison %>%
# filter out exclustions
filter(!gameID %in% df.exclusions$gameID) %>%
# keep only relevant cols
dplyr::select(gameID:level_name_1) %>%
# add phase and puzzle info
mutate(study_phase = factor(study_phase,
levels = c("pretest", "posttest")),
puzzle_id_0 = paste(str_sub(collection_name_0, 1, 7),
level_name_0),
puzzle_id_1 = paste(str_sub(collection_name_1, 1, 7),
level_name_1)) %>%
# keep only relevant cols
dplyr::select(-c(collection_name_0:level_name_1)) %>%
# compute response times
mutate(rt_done2 = rt_done2 - rt_done1,
rt_choose = rt - rt_done2)
df.comparison_processed %>%
head()## # A tibble: 6 × 13
## gameID condition stim_id study_phase trial_type trialNum response
## <chr> <chr> <chr> <fct> <chr> <dbl> <dbl>
## 1 3940-a6a… difficult 679095… pretest sokoban-c… 1 0
## 2 3940-a6a… difficult 679095… pretest sokoban-c… 2 0
## 3 3940-a6a… difficult 679095… pretest sokoban-c… 3 1
## 4 3940-a6a… difficult 679095… pretest sokoban-c… 4 0
## 5 3940-a6a… difficult 679095… pretest sokoban-c… 5 0
## 6 3940-a6a… difficult 679095… pretest sokoban-c… 6 1
## # ℹ 6 more variables: rt <dbl>, rt_done1 <dbl>, rt_done2 <dbl>,
## # puzzle_id_0 <chr>, puzzle_id_1 <chr>, rt_choose <dbl>Create dataset containing all relevant information at once:
df.analysis =
df.game_processed %>%
left_join(df.survey_processed %>%
dplyr::select(gameID,
judgedDifficulty,
participantEffort,
sokobanFamiliarity),
by = "gameID") %>%
left_join(df.metadata %>%
dplyr::select(puzzle_id_num = puzzle_id,
layout,
sokobanonline__solve_rate,
astar_iters, astar_solution_length),
by = "layout") %>%
left_join(df.survey_processed %>%
dplyr::select(gameID,
age = participantYears,
gender = participantGender),
by = "gameID") %>%
mutate(judgedDifficulty = as.numeric(judgedDifficulty),
sokobanFamiliarity = as.numeric(sokobanFamiliarity),
participantEffort = as.numeric(participantEffort)) %>%
dplyr::select(subject_id = gameID,
age, gender,
puzzle_id_sorted, puzzle_id_num,
trialNum, stimuli_set,
layout,
select_response, rating,
solveDuration, solved, boxesSolved,
attempt_nInputEvents, attempt_nRestart, attempt_nUndo,
sokobanonline__solve_rate, astar_iters, astar_solution_length,
judgedDifficulty, mean_difficult,
participantEffort, mean_enjoyable,
sokobanFamiliarity)
df.analysis %>%
head()## # A tibble: 6 × 24
## subject_id age gender puzzle_id_sorted puzzle_id_num trialNum
## <chr> <dbl> <chr> <fct> <dbl> <dbl>
## 1 3940-a6a959f6-… 23 Female Microba 67 0 1
## 2 3940-a6a959f6-… 23 Female Sokogen 13 3 2
## 3 3940-a6a959f6-… 23 Female Sokogen 32 6 3
## 4 3940-a6a959f6-… 23 Female Sokogen 18 9 4
## 5 3940-a6a959f6-… 23 Female Microba 104 12 5
## 6 3940-a6a959f6-… 23 Female Sokogen 38 15 6
## # ℹ 18 more variables: stimuli_set <chr>, layout <chr>,
## # select_response <dbl>, rating <dbl>, solveDuration <dbl>,
## # solved <dbl>, boxesSolved <dbl>, attempt_nInputEvents <dbl>,
## # attempt_nRestart <dbl>, attempt_nUndo <dbl>,
## # sokobanonline__solve_rate <dbl>, astar_iters <dbl>,
## # astar_solution_length <dbl>, judgedDifficulty <dbl>,
## # mean_difficult <dbl>, participantEffort <dbl>, …2 Descriptives
Age by condition:
## # A tibble: 1 × 5
## n M SD min max
## <int> <dbl> <dbl> <dbl> <dbl>
## 1 1640 36.7 12.3 18 74Gender:
## # A tibble: 4 × 2
## gender n
## <chr> <int>
## 1 Female 696
## 2 Male 912
## 3 Non-binary 24
## 4 Prefer not to answer 83 Plots
3.1 % solved per puzzle
df.analysis %>%
group_by(puzzle_id_sorted) %>%
summarise(n = n(),
M = mean(solved),
SD = sd(solved),
min = min(solved),
max = max(solved)) %>%
arrange(desc(M))## # A tibble: 24 × 6
## puzzle_id_sorted n M SD min max
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Dimitri 37 67 0.806 0.398 0 1
## 2 Sokogen 17 67 0.776 0.420 0 1
## 3 Microba 48 67 0.731 0.447 0 1
## 4 Microba 43 70 0.671 0.473 0 1
## 5 Sokogen 14 70 0.671 0.473 0 1
## 6 Sokogen 6 67 0.627 0.487 0 1
## 7 Microba 41 67 0.567 0.499 0 1
## 8 Sokogen 32 68 0.5 0.504 0 1
## 9 Sokogen 13 68 0.471 0.503 0 1
## 10 Microba 26 70 0.443 0.500 0 1
## # ℹ 14 more rowsdf.analysis %>%
filter(!is.na(solved)) %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
group_by(puzzle_id_sorted) %>%
filter(n() > 0) %>%
ungroup() %>%
ggplot(aes(x = factor(puzzle_id_sorted),
y = (solved)*100,
fill = stimuli_set)) +
stat_summary(fun = mean,
geom = "bar",
width = 0.6) +
stat_summary(fun.data = mean_cl_boot,
geom = "errorbar",
width = 0.2) +
scale_y_continuous(limits = c(0, 100),
breaks = seq(0, 100, 25)) +
labs(x = "Puzzle name",
y = "% solved",
title = "% solved per puzzle",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)",
fill = "Puzzle block") +
coord_flip()
3.2 No of boxes solved per puzzle
df.analysis %>%
group_by(puzzle_id_sorted, solved) %>%
summarise(n = n(),
M = mean(boxesSolved),
SD = sd(boxesSolved),
min = min(boxesSolved),
max = max(boxesSolved)) %>%
arrange(desc(M))## # A tibble: 47 × 7
## # Groups: puzzle_id_sorted [24]
## puzzle_id_sorted solved n M SD min max
## <fct> <dbl> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Microba 43 1 47 3 0 3 3
## 2 Dimitri 37 1 54 3 0 3 3
## 3 Microba 48 1 49 3 0 3 3
## 4 Sokogen 14 1 47 3 0 3 3
## 5 Sokogen 17 1 52 3 0 3 3
## 6 Sokogen 6 1 42 3 0 3 3
## 7 Sokogen 32 1 34 3 0 3 3
## 8 Microba 26 1 31 3 0 3 3
## 9 Microba 17 1 25 3 0 3 3
## 10 Microba 41 1 38 3 0 3 3
## # ℹ 37 more rowsdf.analysis %>%
filter(!is.na(solved)) %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
group_by(puzzle_id_sorted) %>%
filter(n() > 0) %>%
ungroup() %>%
ggplot(aes(x = factor(puzzle_id_sorted),
y = boxesSolved)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
width = 0.2,
aes(color = stimuli_set)) +
geom_point(position = position_jitter(height = .05,
width = 0.1),
alpha = .05,
size = 2,
show.legend = FALSE) +
scale_y_continuous(limits = c(0, 3),
breaks = seq(0, 3, 1)) +
labs(x = "Puzzle name",
y = "# of boxes solved",
title = "Number of boxes solved per puzzle (out of 3)",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)",
color = "Puzzle block") +
coord_flip()
3.3 No of actions
df.analysis %>%
group_by(puzzle_id_sorted) %>%
summarise(n = n(),
M = mean(attempt_nInputEvents),
SD = sd(attempt_nInputEvents),
min = min(attempt_nInputEvents),
max = max(attempt_nInputEvents)) %>%
arrange(desc(M))## # A tibble: 24 × 6
## puzzle_id_sorted n M SD min max
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Microba 33 67 265. 129. 43 622
## 2 Sokogen 40 70 236. 139. 22 614
## 3 Microba 104 68 228. 144. 10 608
## 4 Microba 67 68 224. 110. 23 473
## 5 Sokogen 41 70 211. 121. 8 537
## 6 Sokogen 46 70 209. 121. 17 511
## 7 Sokogen 38 68 198. 109. 12 475
## 8 Sokogen 39 67 195. 109. 34 429
## 9 Sokogen 19 67 192. 105. 28 558
## 10 Microba 26 70 190. 126. 23 548
## # ℹ 14 more rowsdf.analysis %>%
filter(!is.na(solved)) %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
group_by(puzzle_id_sorted) %>%
filter(n() > 0) %>%
ungroup() %>%
ggplot(aes(x = factor(puzzle_id_sorted),
y = attempt_nInputEvents)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
width = 0.2,
aes(color = stimuli_set)) +
geom_point(position = position_jitter(height = .05,
width = .1),
alpha = .05,
size = 2,
show.legend = FALSE) +
scale_y_continuous(limits = c(0, 600),
breaks = seq(0, 600, 50)) +
labs(x = "Puzzle name",
y = "# of moves attempted",
title = "Number of moves attempted per puzzle",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)",
color = "Puzzle block") +
coord_flip()
3.4 Time until solution
df.analysis %>%
group_by(puzzle_id_sorted) %>%
summarise(n = n(),
M = mean(solveDuration, na.rm = T),
SD = sd(solveDuration, na.rm = T),
min = min(solveDuration, na.rm = T),
max = max(solveDuration, na.rm = T)) %>%
arrange(desc(M))## # A tibble: 24 × 6
## puzzle_id_sorted n M SD min max
## <fct> <int> <dbl> <dbl> <dbl> <dbl>
## 1 Sokogen 46 70 248. 51.7 160 300
## 2 Microba 104 68 212. 57.5 156 280
## 3 Sokogen 35 68 204. 62.4 82 276
## 4 Sokogen 34 68 197. 58.4 103 299
## 5 Sokogen 40 70 191. 97.8 104 297
## 6 Microba 33 67 191. 82.8 39 295
## 7 Microba 41 67 185. 68.6 63 293
## 8 Sokogen 41 70 184. 64.7 95 297
## 9 Sokogen 39 67 182. 70.1 82 288
## 10 Sokogen 38 68 167. 58.6 81 221
## # ℹ 14 more rowsdf.analysis %>%
filter(!is.na(solved)) %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
group_by(puzzle_id_sorted) %>%
filter(n() > 0) %>%
ungroup() %>%
ggplot(aes(x = factor(puzzle_id_sorted),
y = solveDuration)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
width = 0.2,
aes(color = stimuli_set)) +
geom_point(position = position_jitter(height = .05,
width = .1),
size = 2,
alpha = .05,
show.legend = FALSE) +
scale_y_continuous(limits = c(0, 300),
breaks = seq(0, 300, 60)) +
labs(x = "Puzzle name",
y = "Time until solution (in sec)",
title = "Time until solution per puzzle",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)",
color = "Puzzle block") +
coord_flip()
4 Modeling
4.1 Improvement over time
4.1.1 Performance on first half of puzzles vs last half of puzzles
Do people generally become better at Sokoban over time?
I.e., do we see differences in performance metrics (% solved, boxes solved, time until solution, number of steps) when we compare the first four puzzles people solved, vs the last four puzzles people solved?
4.1.1.1 % solved
df.analysis %>%
mutate(trialNum = case_when(trialNum > 4 ~ "Last half of puzzles",
trialNum <= 4 ~ "First half of puzzles"),
puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
filter(!is.na(trialNum)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = (solved)*100,
fill = trialNum)) +
stat_summary(fun = mean,
geom = "bar",
width = .6,
position = position_dodge(.8)) +
stat_summary(fun.data = mean_cl_boot,
geom = "errorbar",
position = position_dodge(.8)) +
scale_y_continuous(limits = c(0, 100),
breaks = seq(0, 100, 25)) +
labs(x = "Puzzle Name",
y = "% solved",
title = "% solved over time (first vs last half of puzzle set)",
subtitle = "8 puzzles per set",
fill = "Stage") +
coord_flip()
Do we see a progression in % solved when we break it down by puzzle order?
df.analysis %>%
group_by(trialNum, puzzle_id_sorted) %>%
summarise(mean = mean(solved)) %>%
ggplot(aes(x = trialNum,
y = (mean*100),
color = puzzle_id_sorted)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .4) +
labs(x = "Puzzle order (1 through 8)",
y = "% solved",
title = "% solved over time",
fill = "Puzzle") +
theme(legend.position = "none") +
scale_x_continuous(breaks = seq(1,8,1))
Fitting the mixed effects model:
# mixed effects model
lm.pct_solved_order =
glmer(solved ~
1 +
# fixed effect for puzzle order
trialNum +
# controlling for other variables
sokobanonline__solve_rate + # difficulty
participantEffort + # subjective effort
attempt_nRestart + # no of attempts
mean_enjoyable + # sampled enjoyment ratings
# random intercept for player
(1 | subject_id),
family = binomial(link = "logit"),
data = df.analysis)
# summary
lm.pct_solved_order %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula:
## solved ~ 1 + trialNum + sokobanonline__solve_rate + participantEffort +
## attempt_nRestart + mean_enjoyable + (1 | subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 1280.9 1318.7 -633.5 1266.9 1633
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -7.4776 -0.2921 -0.1021 0.2233 14.9158
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 5.921 2.433
## Number of obs: 1640, groups: subject_id, 205
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -4.77692 2.05322 -2.327 0.020 *
## trialNum -0.16298 0.03925 -4.153 3.29e-05 ***
## sokobanonline__solve_rate 0.82759 1.38413 0.598 0.550
## participantEffort -0.19478 0.37544 -0.519 0.604
## attempt_nRestart -0.59827 0.05025 -11.905 < 2e-16 ***
## mean_enjoyable 1.21227 0.10574 11.464 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm skb___ prtcpE attm_R
## trialNum -0.034
## skbnnln__s_ -0.363 -0.183
## prtcpntEffr -0.889 0.031 0.012
## attmpt_nRst -0.098 0.224 0.017 0.060
## mean_enjybl -0.061 -0.004 -0.441 -0.009 -0.176
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00203212 (tol = 0.002, component 1)## $trialNum
## # Predicted probabilities of solved
##
## trialNum | Predicted | 95% CI
## ---------------------------------
## 1 | 0.45 | 0.46, 0.51
## 2 | 0.43 | 0.45, 0.51
## 3 | 0.40 | 0.45, 0.50
## 4 | 0.38 | 0.43, 0.50
## 5 | 0.35 | 0.42, 0.49
## 6 | 0.32 | 0.40, 0.48
## 7 | 0.29 | 0.37, 0.48
## 8 | 0.27 | 0.34, 0.47
##
## Adjusted for:
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $sokobanonline__solve_rate
## # Predicted probabilities of solved
##
## sokobanonline__solve_rate | Predicted | 95% CI
## --------------------------------------------------
## 0.40 | 0.32 | 0.30, 0.51
## 0.60 | 0.35 | 0.40, 0.50
## 0.80 | 0.38 | 0.43, 0.50
## 1.00 | 0.40 | 0.39, 0.52
##
## Adjusted for:
## * trialNum = 4.50
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $participantEffort
## # Predicted probabilities of solved
##
## participantEffort | Predicted | 95% CI
## ------------------------------------------
## 1 | 0.46 | 0.12, 0.85
## 3 | 0.42 | 0.30, 0.59
## 4 | 0.39 | 0.40, 0.51
## 5 | 0.36 | 0.42, 0.49
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $attempt_nRestart
## # Predicted probabilities of solved
##
## attempt_nRestart | Predicted | 95% CI
## -----------------------------------------
## 0 | 0.57 | 0.49, 0.55
## 3 | 0.43 | 0.46, 0.50
## 6 | 0.15 | 0.22, 0.38
## 9 | 0.03 | 0.04, 0.13
## 11 | 0.01 | 0.01, 0.05
## 14 | 0.00 | 0.00, 0.01
## 17 | 0.00 | 0.00, 0.00
## 23 | 0.00 | 0.00, 0.00
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)##
## $mean_enjoyable
## # Predicted probabilities of solved
##
## mean_enjoyable | Predicted | 95% CI
## ---------------------------------------
## 3.50 | 0.05 | 0.08, 0.20
## 4.00 | 0.09 | 0.14, 0.29
## 4.50 | 0.16 | 0.23, 0.38
## 5.00 | 0.25 | 0.33, 0.45
## 6.00 | 0.44 | 0.46, 0.51
## 6.50 | 0.49 | 0.48, 0.52
## 7.00 | 0.52 | 0.48, 0.53
## 8.00 | 0.68 | 0.51, 0.63
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * subject_id = 0 (population-level)##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.1.1.2 Boxes solved
df.analysis %>%
mutate(trialNum = case_when(trialNum > 4 ~ "Last half of puzzles",
trialNum <= 4 ~ "First half of puzzles"),
puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
filter(!is.na(trialNum)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = boxesSolved,
color = trialNum)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
position = position_dodge(.8)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .1) +
scale_y_continuous(limits = c(0, 3),
breaks = seq(0,3,1)) +
labs(x = "Puzzle name",
y = "# of boxes solved (0-3)",
title = "# of boxes solved over time (first vs last half of puzzle set)",
subtitle = "8 puzzles per set",
color = "Stage") +
coord_flip()
When broken down by individual puzzle:
df.analysis %>%
group_by(trialNum, puzzle_id_sorted) %>%
summarise(mean = mean(boxesSolved)) %>%
ggplot(aes(x = trialNum,
y = mean,
color = puzzle_id_sorted)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .4) +
labs(x = "Puzzle order (1 through 8)",
y = "Mean # of boxes solved",
title = "Mean # of boxes solved over time",
fill = "Puzzle") +
theme(legend.position = "none") +
scale_x_continuous(breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0,3),
breaks = seq(0,3,1))
Fitting the mixed effects model:
# mixed effects model
lm.number_solved_order =
glmer(boxesSolved ~
1 +
# fixed effect for puzzle order (controlling for difficulty)
trialNum +
# controlling for other variables
sokobanonline__solve_rate + # difficulty
participantEffort + # subjective effort
attempt_nRestart + # no of attempts
mean_enjoyable + # sampled enjoyment ratings
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
# summary
lm.number_solved_order %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## boxesSolved ~ 1 + trialNum + sokobanonline__solve_rate + participantEffort +
## attempt_nRestart + mean_enjoyable + (1 | subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 4749.4 4787.2 -2367.7 4735.4 1633
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.6507 -0.3346 0.1122 0.2824 1.1029
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 0 0
## Number of obs: 1640, groups: subject_id, 205
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.285440 0.239226 1.193 0.23280
## trialNum -0.017090 0.007604 -2.248 0.02460 *
## sokobanonline__solve_rate -0.059276 0.264522 -0.224 0.82269
## participantEffort -0.005799 0.033906 -0.171 0.86421
## attempt_nRestart -0.016475 0.005364 -3.071 0.00213 **
## mean_enjoyable 0.116786 0.015963 7.316 2.55e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm skb___ prtcpE attm_R
## trialNum -0.079
## skbnnln__s_ -0.611 -0.119
## prtcpntEffr -0.705 0.004 0.026
## attmpt_nRst -0.268 0.092 0.032 0.094
## mean_enjybl 0.039 0.066 -0.540 -0.016 0.228
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## $trialNum
## # Predicted counts of boxesSolved
##
## trialNum | Predicted | 95% CI
## ---------------------------------
## 1 | 2.19 | 2.06, 2.33
## 2 | 2.16 | 2.05, 2.27
## 3 | 2.12 | 2.04, 2.21
## 4 | 2.08 | 2.01, 2.16
## 5 | 2.05 | 1.98, 2.12
## 6 | 2.01 | 1.93, 2.10
## 7 | 1.98 | 1.88, 2.08
## 8 | 1.95 | 1.83, 2.07
##
## Adjusted for:
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $sokobanonline__solve_rate
## # Predicted counts of boxesSolved
##
## sokobanonline__solve_rate | Predicted | 95% CI
## --------------------------------------------------
## 0.40 | 2.11 | 1.77, 2.51
## 0.60 | 2.08 | 1.93, 2.25
## 0.80 | 2.06 | 1.96, 2.16
## 1.00 | 2.03 | 1.76, 2.35
##
## Adjusted for:
## * trialNum = 4.50
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $participantEffort
## # Predicted counts of boxesSolved
##
## participantEffort | Predicted | 95% CI
## ------------------------------------------
## 1 | 2.11 | 1.64, 2.73
## 3 | 2.09 | 1.84, 2.36
## 4 | 2.08 | 1.95, 2.21
## 5 | 2.06 | 1.99, 2.14
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $attempt_nRestart
## # Predicted counts of boxesSolved
##
## attempt_nRestart | Predicted | 95% CI
## -----------------------------------------
## 0 | 2.20 | 2.09, 2.31
## 3 | 2.09 | 2.02, 2.17
## 6 | 1.99 | 1.91, 2.08
## 9 | 1.89 | 1.77, 2.02
## 11 | 1.83 | 1.68, 2.00
## 14 | 1.75 | 1.56, 1.96
## 17 | 1.66 | 1.44, 1.92
## 23 | 1.50 | 1.22, 1.85
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)##
## $mean_enjoyable
## # Predicted counts of boxesSolved
##
## mean_enjoyable | Predicted | 95% CI
## ---------------------------------------
## 3.50 | 1.62 | 1.50, 1.75
## 4.00 | 1.72 | 1.62, 1.83
## 4.50 | 1.82 | 1.73, 1.92
## 5.00 | 1.93 | 1.86, 2.01
## 6.00 | 2.17 | 2.10, 2.25
## 6.50 | 2.30 | 2.21, 2.40
## 7.00 | 2.44 | 2.32, 2.57
## 8.00 | 2.74 | 2.54, 2.97
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * subject_id = 0 (population-level)##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.1.1.3 Time spent
df.analysis %>%
mutate(trialNum = case_when(trialNum > 4 ~ "Last half of puzzles",
trialNum <= 4 ~ "First half of puzzles"),
puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
filter(!is.na(trialNum)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = solveDuration,
color = trialNum)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
position = position_dodge(.8)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .1) +
scale_y_continuous(limits = c(0, 300),
breaks = seq(0,300,60)) +
labs(x = "Puzzle name",
y = "# of boxes solved (0-3)",
title = "# of boxes solved over time (first vs last half of puzzle set)",
subtitle = "8 puzzles per set",
color = "Stage") +
coord_flip()
When broken down by puzzle:
df.analysis %>%
group_by(trialNum, puzzle_id_sorted) %>%
summarise(mean = mean(solveDuration, na.rm = T)) %>%
ggplot(aes(x = trialNum,
y = mean,
color = puzzle_id_sorted)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .4) +
labs(x = "Puzzle order (1 through 8)",
y = "Mean solve time",
title = "Mean solve time over time",
fill = "Puzzle") +
theme(legend.position = "none") +
scale_x_continuous(breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0,300),
breaks = seq(0,300,60))
Fitting the mixed effects model:
# mixed effects model
lm.duration_order =
glmer(solveDuration ~
1 +
# fixed effect for puzzle order (controlling for difficulty)
trialNum +
# controlling for other variables
sokobanonline__solve_rate + # difficulty
participantEffort + # subjective effort
attempt_nRestart + # no of attempts
mean_enjoyable + # sampled enjoyment ratings
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
# summary
lm.duration_order %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## solveDuration ~ 1 + trialNum + sokobanonline__solve_rate + participantEffort +
## attempt_nRestart + mean_enjoyable + (1 | subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 12964.6 12995.4 -6475.3 12950.6 587
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -9.3608 -2.5398 -0.1669 2.1638 12.1721
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 0.1815 0.426
## Number of obs: 594, groups: subject_id, 170
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 4.565125 0.309418 14.754 < 2e-16 ***
## trialNum 0.040476 0.001880 21.531 < 2e-16 ***
## sokobanonline__solve_rate -0.040827 0.063534 -0.643 0.52048
## participantEffort 0.165448 0.063269 2.615 0.00892 **
## attempt_nRestart 0.145349 0.002033 71.502 < 2e-16 ***
## mean_enjoyable -0.137998 0.004647 -29.698 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm skb___ prtcpE attm_R
## trialNum -0.022
## skbnnln__s_ -0.122 0.002
## prtcpntEffr -0.985 0.002 0.014
## attmpt_nRst -0.066 0.161 0.106 0.024
## mean_enjybl 0.000 -0.092 -0.516 -0.013 0.065
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0027371 (tol = 0.002, component 1)## $trialNum
## # Predicted counts of solveDuration
##
## trialNum | Predicted | 95% CI
## -------------------------------------
## 1 | 119.42 | 112.17, 127.96
## 2 | 124.35 | 116.87, 133.17
## 3 | 129.49 | 121.75, 138.62
## 4 | 134.83 | 126.80, 144.32
## 5 | 140.40 | 132.04, 150.28
## 6 | 146.20 | 137.46, 156.53
## 7 | 152.24 | 143.07, 163.06
## 8 | 158.53 | 148.88, 169.91
##
## Adjusted for:
## * sokobanonline__solve_rate = 0.76
## * participantEffort = 4.83
## * attempt_nRestart = 1.98
## * mean_enjoyable = 6.39
## * subject_id = 0 (population-level)
##
## $sokobanonline__solve_rate
## # Predicted counts of solveDuration
##
## sokobanonline__solve_rate | Predicted | 95% CI
## ------------------------------------------------------
## 0.60 | 137.96 | 129.34, 148.12
## 0.70 | 137.40 | 129.15, 147.13
## 0.80 | 136.84 | 128.67, 146.48
## 0.90 | 136.28 | 127.88, 146.19
##
## Adjusted for:
## * trialNum = 4.41
## * participantEffort = 4.83
## * attempt_nRestart = 1.98
## * mean_enjoyable = 6.39
## * subject_id = 0 (population-level)
##
## $participantEffort
## # Predicted counts of solveDuration
##
## participantEffort | Predicted | 95% CI
## ----------------------------------------------
## 1 | 72.77 | 45.33, 117.60
## 3 | 101.32 | 80.49, 128.37
## 4 | 119.55 | 106.45, 135.13
## 5 | 141.06 | 132.10, 151.61
##
## Adjusted for:
## * trialNum = 4.41
## * sokobanonline__solve_rate = 0.76
## * attempt_nRestart = 1.98
## * mean_enjoyable = 6.39
## * subject_id = 0 (population-level)
##
## $attempt_nRestart
## # Predicted counts of solveDuration
##
## attempt_nRestart | Predicted | 95% CI
## ---------------------------------------------
## 0 | 102.82 | 96.63, 110.12
## 2 | 137.50 | 129.31, 147.17
## 3 | 159.01 | 149.54, 170.20
## 5 | 212.66 | 199.83, 227.79
## 7 | 284.40 | 266.79, 305.17
## 8 | 328.90 | 308.16, 353.33
## 10 | 439.85 | 410.89, 473.95
## 13 | 680.27 | 631.79, 737.27
##
## Adjusted for:
## * trialNum = 4.41
## * sokobanonline__solve_rate = 0.76
## * participantEffort = 4.83
## * mean_enjoyable = 6.39
## * subject_id = 0 (population-level)##
## $mean_enjoyable
## # Predicted counts of solveDuration
##
## mean_enjoyable | Predicted | 95% CI
## -------------------------------------------
## 4.00 | 190.53 | 178.57, 204.61
## 4.40 | 180.29 | 169.16, 193.42
## 5.00 | 165.97 | 155.91, 177.84
## 5.40 | 157.05 | 147.62, 168.19
## 5.80 | 148.62 | 139.74, 159.10
## 6.40 | 136.81 | 128.66, 146.43
## 6.80 | 129.46 | 121.74, 138.58
## 7.80 | 112.78 | 105.91, 120.87
##
## Adjusted for:
## * trialNum = 4.41
## * sokobanonline__solve_rate = 0.76
## * participantEffort = 4.83
## * attempt_nRestart = 1.98
## * subject_id = 0 (population-level)##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.1.1.4 No of moves
df.analysis %>%
mutate(trialNum = case_when(trialNum > 4 ~ "Last half of puzzles",
trialNum <= 4 ~ "First half of puzzles"),
puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE)) %>%
filter(!is.na(trialNum)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = attempt_nInputEvents,
color = trialNum)) +
stat_summary(fun.data = mean_cl_boot,
geom = "pointrange",
position = position_dodge(.8)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .1) +
labs(x = "Puzzle name",
y = "# of moves",
title = "# of moves over time (first vs last half of puzzle set)",
subtitle = "8 puzzles per set",
color = "Stage") +
coord_flip()
When broken down by puzzle:
df.analysis %>%
group_by(trialNum, puzzle_id_sorted) %>%
summarise(mean = mean(attempt_nInputEvents, na.rm = T)) %>%
ggplot(aes(x = trialNum,
y = mean,
color = puzzle_id_sorted)) +
geom_point(position = position_jitter(width = .1,
height = .1),
size = 2,
alpha = .4) +
labs(x = "Puzzle order (1 through 8)",
y = "Mean # of moves",
title = "Mean # of moves over time",
fill = "Puzzle") +
theme(legend.position = "none") +
scale_x_continuous(breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0, 600),
breaks = seq(0,600,100))
Fitting the mixed effects model:
# mixed effects model
lm.moves_order =
glmer(attempt_nInputEvents ~
1 +
# fixed effect for puzzle order (controlling for difficulty)
trialNum +
# controlling for other variables
scale(sokobanonline__solve_rate) + # difficulty
scale(participantEffort) + # subjective effort
scale(attempt_nRestart) + # no of attempts
scale(mean_enjoyable) + # sampled enjoyment ratings
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
# summary
lm.moves_order %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## attempt_nInputEvents ~ 1 + trialNum + scale(sokobanonline__solve_rate) +
## scale(participantEffort) + scale(attempt_nRestart) + scale(mean_enjoyable) +
## (1 | subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 50770.1 50807.9 -25378.1 50756.1 1633
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -13.2862 -3.4381 -0.3989 3.1754 21.8264
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 0.1335 0.3654
## Number of obs: 1640, groups: subject_id, 205
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 5.1087677 0.0258687 197.488
## trialNum -0.0132728 0.0008333 -15.928
## scale(sokobanonline__solve_rate) -0.0764573 0.0024735 -30.910
## scale(participantEffort) -0.0404824 0.0255909 -1.582
## scale(attempt_nRestart) 0.2341045 0.0023987 97.595
## scale(mean_enjoyable) -0.0418659 0.0028627 -14.625
## Pr(>|z|)
## (Intercept) <2e-16 ***
## trialNum <2e-16 ***
## scale(sokobanonline__solve_rate) <2e-16 ***
## scale(participantEffort) 0.114
## scale(attempt_nRestart) <2e-16 ***
## scale(mean_enjoyable) <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm s(___) scl(E) sc(_R)
## trialNum -0.142
## scl(skb___) 0.037 -0.228
## scl(prtcpE) 0.000 0.000 0.002
## scl(ttmp_R) -0.024 0.102 -0.026 0.009
## scl(mn_njy) -0.020 0.159 -0.581 0.000 0.310
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?## $trialNum
## # Predicted counts of attempt_nInputEvents
##
## trialNum | Predicted | 95% CI
## -------------------------------------
## 1 | 163.74 | 156.11, 172.70
## 2 | 161.58 | 154.08, 170.40
## 3 | 159.45 | 152.06, 168.14
## 4 | 157.35 | 150.07, 165.91
## 5 | 155.27 | 148.09, 163.72
## 6 | 153.23 | 146.13, 161.57
## 7 | 151.21 | 144.18, 159.46
## 8 | 149.21 | 142.26, 157.38
##
## Adjusted for:
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $sokobanonline__solve_rate
## # Predicted counts of attempt_nInputEvents
##
## sokobanonline__solve_rate | Predicted | 95% CI
## ------------------------------------------------------
## 0.40 | 216.77 | 205.90, 229.48
## 0.60 | 177.88 | 169.54, 187.67
## 0.80 | 145.96 | 139.18, 153.94
## 1.00 | 119.78 | 113.91, 126.65
##
## Adjusted for:
## * trialNum = 4.50
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $participantEffort
## # Predicted counts of attempt_nInputEvents
##
## participantEffort | Predicted | 95% CI
## ----------------------------------------------
## 1 | 210.89 | 145.43, 307.52
## 3 | 180.17 | 150.46, 216.96
## 4 | 166.53 | 152.14, 183.30
## 5 | 153.93 | 146.29, 162.87
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * attempt_nRestart = 3.76
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)
##
## $attempt_nRestart
## # Predicted counts of attempt_nInputEvents
##
## attempt_nRestart | Predicted | 95% CI
## ---------------------------------------------
## 0.00 | 122.03 | 116.35, 128.71
## 3.00 | 148.70 | 141.82, 156.79
## 6.00 | 181.20 | 172.80, 191.06
## 9.00 | 220.79 | 210.48, 232.90
## 11.00 | 251.88 | 240.03, 265.80
## 14.00 | 306.92 | 292.23, 324.16
## 17.00 | 373.99 | 355.68, 395.45
## 23.00 | 555.30 | 526.50, 588.94
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * mean_enjoyable = 5.57
## * subject_id = 0 (population-level)##
## $mean_enjoyable
## # Predicted counts of attempt_nInputEvents
##
## mean_enjoyable | Predicted | 95% CI
## -------------------------------------------
## 3.50 | 167.18 | 159.32, 176.42
## 4.00 | 164.48 | 156.80, 173.51
## 4.50 | 161.83 | 154.31, 170.67
## 5.00 | 159.22 | 151.84, 167.89
## 6.00 | 154.12 | 146.98, 162.51
## 6.50 | 151.63 | 144.59, 159.91
## 7.00 | 149.19 | 142.22, 157.37
## 8.00 | 144.41 | 137.57, 152.44
##
## Adjusted for:
## * trialNum = 4.50
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * subject_id = 0 (population-level)##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.2 Success on preceding puzzle
Is past performance a good predictor of future performance?
df.analysis =
df.analysis %>%
mutate(prev_puzzle_solved = lag(solved))
df.analysis %>%
mutate(puzzle_id_sorted = fct_reorder(puzzle_id_sorted,
solved,
.fun = mean, .na_rm = TRUE),
prev_puzzle_solved = case_when(prev_puzzle_solved == 1 ~ "Yes",
prev_puzzle_solved == 0 ~ "No")) %>%
filter(!is.na(prev_puzzle_solved)) %>%
ggplot(aes(x = puzzle_id_sorted,
y = (solved * 100),
fill = factor(prev_puzzle_solved))) +
stat_summary(fun = mean,
geom = "bar",
width = .6,
alpha = .5,
position = position_dodge(.8)) +
stat_summary(fun.data = mean_cl_boot,
geom = "errorbar",
position = position_dodge(.8)) +
scale_fill_manual(values = c("Yes" = "darkgreen",
"No" = "darkred")) +
labs(x = "Puzzle name",
y = "% solved",
fill = "Last puzzle solved?",
title = "% solved by previous puzzle success",
subtitle = "N = 205 subjects, 24 puzzles total (n = 67-70 each)") +
coord_flip() +
theme(legend.position = "right")
Fitting the mixed effects model:
# mixed effects model
lm.previous_performance =
glmer(solved ~
1 +
# fixed effect for previous puzzle solved
prev_puzzle_solved +
# controlling for other variables
scale(sokobanonline__solve_rate) + # difficulty
scale(participantEffort) + # subjective effort
scale(attempt_nRestart) + # no of attempts
# random intercept for player
(1 | subject_id),
family = poisson(link = "log"),
data = df.analysis)
# summary
lm.previous_performance %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## solved ~ 1 + prev_puzzle_solved + scale(sokobanonline__solve_rate) +
## scale(participantEffort) + scale(attempt_nRestart) + (1 |
## subject_id)
## Data: df.analysis
##
## AIC BIC logLik deviance df.resid
## 2133.3 2165.7 -1060.7 2121.3 1633
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -0.9832 -0.4917 -0.3317 0.3886 4.7142
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject_id (Intercept) 0.1745 0.4177
## Number of obs: 1639, groups: subject_id, 205
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) -1.456309 0.073308 -19.865
## prev_puzzle_solved 0.259869 0.088379 2.940
## scale(sokobanonline__solve_rate) 0.237241 0.041138 5.767
## scale(participantEffort) -0.008423 0.052765 -0.160
## scale(attempt_nRestart) -0.751607 0.070664 -10.636
## Pr(>|z|)
## (Intercept) < 2e-16 ***
## prev_puzzle_solved 0.00328 **
## scale(sokobanonline__solve_rate) 8.07e-09 ***
## scale(participantEffort) 0.87318
## scale(attempt_nRestart) < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) prv_p_ s(___) scl(E)
## prv_pzzl_sl -0.430
## scl(skb___) -0.109 0.084
## scl(prtcpE) 0.018 -0.026 0.010
## scl(ttmp_R) 0.400 0.107 0.219 0.058## $prev_puzzle_solved
## # Predicted counts of solved
##
## prev_puzzle_solved | Predicted | 95% CI
## -------------------------------------------
## 0 | 0.39 | 0.56, 0.74
## 1 | 0.50 | 0.71, 0.98
##
## Adjusted for:
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * subject_id = 0 (population-level)
##
## $sokobanonline__solve_rate
## # Predicted counts of solved
##
## sokobanonline__solve_rate | Predicted | 95% CI
## --------------------------------------------------
## 0.40 | 0.15 | 0.17, 0.38
## 0.60 | 0.28 | 0.39, 0.58
## 0.80 | 0.53 | 0.77, 1.00
## 1.00 | 0.97 | 1.21, 2.16
##
## Adjusted for:
## * prev_puzzle_solved = 0.36
## * participantEffort = 4.80
## * attempt_nRestart = 3.76
## * subject_id = 0 (population-level)
##
## $participantEffort
## # Predicted counts of solved
##
## participantEffort | Predicted | 95% CI
## ------------------------------------------
## 1 | 0.45 | 0.34, 1.64
## 3 | 0.44 | 0.50, 1.07
## 4 | 0.43 | 0.58, 0.88
## 5 | 0.42 | 0.62, 0.80
##
## Adjusted for:
## * prev_puzzle_solved = 0.36
## * sokobanonline__solve_rate = 0.73
## * attempt_nRestart = 3.76
## * subject_id = 0 (population-level)
##
## $attempt_nRestart
## # Predicted counts of solved
##
## attempt_nRestart | Predicted | 95% CI
## -----------------------------------------
## 0.00 | 0.94 | 1.36, 1.80
## 3.00 | 0.50 | 0.74, 0.93
## 6.00 | 0.26 | 0.37, 0.53
## 9.00 | 0.14 | 0.18, 0.31
## 11.00 | 0.09 | 0.11, 0.22
## 14.00 | 0.05 | 0.05, 0.13
## 17.00 | 0.03 | 0.02, 0.08
## 23.00 | 0.01 | 0.01, 0.03
##
## Adjusted for:
## * prev_puzzle_solved = 0.36
## * sokobanonline__solve_rate = 0.73
## * participantEffort = 4.80
## * subject_id = 0 (population-level)##
## attr(,"class")
## [1] "ggalleffects" "list"
## attr(,"model.name")
## [1] "."4.3 Growth curve model
% solved:
# null model: no learning over time
lm.solve_growth_null =
glmer(solved ~
1 +
# control vars
scale(astar_solution_length) +
scale(sokobanonline__solve_rate) +
(1 | puzzle_id_sorted) +
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = binomial(link = "logit"),
control = glmerControl(optimizer = "bobyqa"))
lm.solve_growth =
glmer(solved ~
1 +
# fixed effect
trialNum +
# control vars
scale(astar_solution_length) +
scale(sokobanonline__solve_rate) +
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = binomial(link = "logit"),
control = glmerControl(optimizer = "bobyqa"))
lm.solve_growth %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula:
## solved ~ 1 + trialNum + scale(astar_solution_length) + scale(sokobanonline__solve_rate) +
## (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## Data: df.analysis
## Control: glmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 1534.5 1577.7 -759.2 1518.5 1632
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.2814 -0.4325 -0.1487 0.4017 7.7285
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subject_id (Intercept) 1.919467 1.38545
## trialNum 0.008961 0.09466 1.00
## puzzle_id_sorted (Intercept) 2.331166 1.52682
## Number of obs: 1640, groups: subject_id, 205; puzzle_id_sorted, 24
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) -1.1882399 0.0009211 -1289.964
## trialNum -0.0078792 0.0009242 -8.526
## scale(astar_solution_length) -0.8155390 0.0009212 -885.281
## scale(sokobanonline__solve_rate) 0.9974857 0.0009212 1082.787
## Pr(>|z|)
## (Intercept) <2e-16 ***
## trialNum <2e-16 ***
## scale(astar_solution_length) <2e-16 ***
## scale(sokobanonline__solve_rate) <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm sc(__)
## trialNum 0.000
## scl(str_s_) 0.000 0.000
## scl(skb___) 0.000 0.000 0.000
## optimizer (bobyqa) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.0770368 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?## Data: df.analysis
## Models:
## lm.solve_growth_null: solved ~ 1 + scale(astar_solution_length) + scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## lm.solve_growth: solved ~ 1 + trialNum + scale(astar_solution_length) + scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.solve_growth_null 7 1532.5 1570.3 -759.25 1518.5
## lm.solve_growth 8 1534.5 1577.7 -759.24 1518.5 0.0184 1
## Pr(>Chisq)
## lm.solve_growth_null
## lm.solve_growth 0.892df.analysis$predicted_solve =
predict(lm.solve_growth, type = "response")
df.analysis_subject =
df.analysis %>%
group_by(subject_id, trialNum) %>%
summarise(mean_pred = mean(predicted_solve, na.rm = TRUE),
.groups = "drop")
df.analysis_subject %>%
ggplot(aes(x = trialNum,
y = (mean_pred*100))) +
geom_line(aes(group = subject_id),
alpha = 0.1, color = "gray") + # individual trajectories
stat_summary(fun = mean,
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun.data = mean_cl_boot,
geom = "ribbon",
aes(group = 1),
fill = "#1f77b4",
alpha = 0.2) +
labs(x = "Puzzle #",
y = "% solved",
title = "Predicted performance curves across puzzles: % solved",
subtitle = "Grey lines are individual subjects, blue line and ribbon equal predicted mean + 95% CI") +
scale_x_continuous(limits = c(1, 8),
breaks = seq(1,8,1)) +
theme_minimal()
boxes solved:
# null model: no learning over time
lm.boxes_growth_null =
glmer(boxesSolved ~
1 +
# control vars
scale(astar_solution_length) +
scale(sokobanonline__solve_rate) +
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))# full model:
lm.boxes_growth =
glmer(boxesSolved ~
1 +
trialNum +
# control vars
scale(astar_solution_length) +
scale(sokobanonline__solve_rate) +
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))
lm.boxes_growth %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## boxesSolved ~ 1 + trialNum + scale(astar_solution_length) + scale(sokobanonline__solve_rate) +
## (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## Data: df.analysis
## Control: glmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 4750.5 4793.8 -2367.3 4734.5 1632
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.58271 -0.24067 0.01022 0.38199 1.47835
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subject_id (Intercept) 0.000e+00 0.000e+00
## trialNum 6.955e-15 8.340e-08 NaN
## puzzle_id_sorted (Intercept) 2.985e-02 1.728e-01
## Number of obs: 1640, groups: subject_id, 205; puzzle_id_sorted, 24
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 0.7148071 0.0568420 12.575
## trialNum 0.0007999 0.0091031 0.088
## scale(astar_solution_length) -0.1192187 0.0421645 -2.827
## scale(sokobanonline__solve_rate) 0.0600862 0.0409598 1.467
## Pr(>|z|)
## (Intercept) < 2e-16 ***
## trialNum 0.92998
## scale(astar_solution_length) 0.00469 **
## scale(sokobanonline__solve_rate) 0.14239
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm sc(__)
## trialNum -0.721
## scl(str_s_) 0.182 -0.227
## scl(skb___) 0.085 -0.130 0.262
## optimizer (bobyqa) convergence code: 0 (OK)
## boundary (singular) fit: see help('isSingular')## Data: df.analysis
## Models:
## lm.boxes_growth_null: boxesSolved ~ 1 + scale(astar_solution_length) + scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## lm.boxes_growth: boxesSolved ~ 1 + trialNum + scale(astar_solution_length) + scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.boxes_growth_null 7 4748.5 4786.4 -2367.3 4734.5
## lm.boxes_growth 8 4750.5 4793.8 -2367.3 4734.5 0.0077 1
## Pr(>Chisq)
## lm.boxes_growth_null
## lm.boxes_growth 0.93df.analysis$predicted_boxes =
predict(lm.boxes_growth, type = "response")
df.analysis_subject =
df.analysis %>%
group_by(subject_id, trialNum) %>%
summarise(mean_pred = mean(predicted_boxes, na.rm = TRUE),
.groups = "drop")
df.analysis_subject %>%
ggplot(aes(x = trialNum,
y = mean_pred)) +
geom_line(aes(group = subject_id),
alpha = 0.1, color = "gray") + # individual trajectories
stat_summary(fun = mean,
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun = "errorbar",
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun.data = mean_cl_boot,
geom = "ribbon",
aes(group = 1),
fill = "#1f77b4",
alpha = 0.2) +
labs(x = "Puzzle #",
y = "# of boxes solved",
title = "Predicted performance curves across puzzles: # of boxes solved",
subtitle = "Grey lines are individual subjects, blue line and ribbon equal predicted mean + 95% CI") +
scale_x_continuous(limits = c(1, 8),
breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0, 3),
breaks = seq(0,3, 1)) +
theme_minimal()
time to solution:
# null model: no learning over time
lm.time_growth_null =
glmer(solveDuration ~
1 +
# control vars
scale(astar_solution_length) +
scale(sokobanonline__solve_rate) +
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))# full model:
lm.time_growth =
glmer(solveDuration ~
1 +
trialNum +
# control vars
scale(astar_solution_length) +
scale(sokobanonline__solve_rate) +
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))
lm.time_growth %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## solveDuration ~ 1 + trialNum + scale(astar_solution_length) +
## scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) +
## (1 + trialNum | subject_id)
## Data: df.analysis
## Control: glmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 13086.4 13121.5 -6535.2 13070.4 586
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -9.7288 -2.2713 -0.0644 1.6028 12.9155
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subject_id (Intercept) 0.83419 0.9133
## trialNum 0.03509 0.1873 -0.87
## puzzle_id_sorted (Intercept) 0.07271 0.2697
## Number of obs: 594, groups: subject_id, 170; puzzle_id_sorted, 23
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 5.26628 0.09455 55.700 < 2e-16
## trialNum -0.04062 0.01589 -2.556 0.01057
## scale(astar_solution_length) 0.16312 0.05952 2.741 0.00613
## scale(sokobanonline__solve_rate) -0.09956 0.06091 -1.635 0.10215
##
## (Intercept) ***
## trialNum *
## scale(astar_solution_length) **
## scale(sokobanonline__solve_rate)
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm sc(__)
## trialNum -0.699
## scl(str_s_) 0.051 -0.014
## scl(skb___) -0.045 -0.008 0.143## Data: df.analysis
## Models:
## lm.time_growth_null: solveDuration ~ 1 + scale(astar_solution_length) + scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## lm.time_growth: solveDuration ~ 1 + trialNum + scale(astar_solution_length) + scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.time_growth_null 7 13091 13122 -6538.4 13077
## lm.time_growth 8 13086 13122 -6535.2 13070 6.48 1
## Pr(>Chisq)
## lm.time_growth_null
## lm.time_growth 0.01091 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1df.analysis =
df.analysis %>%
mutate(predicted_time = NA_real_)
df.analysis$predicted_time[df.analysis$solved == 1] =
predict(lm.time_growth, type = "response")
df.analysis_subject =
df.analysis %>%
group_by(subject_id, trialNum) %>%
summarise(mean_pred = mean(predicted_time, na.rm = TRUE),
.groups = "drop")
df.analysis_subject %>%
ggplot(aes(x = trialNum,
y = mean_pred)) +
geom_line(aes(group = subject_id),
alpha = 0.1, color = "gray") + # individual trajectories
stat_summary(fun = mean,
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun = "errorbar",
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun.data = mean_cl_boot,
geom = "ribbon",
aes(group = 1),
fill = "#1f77b4",
alpha = 0.2) +
labs(x = "Puzzle #",
y = "Time until solution",
title = "Predicted performance curves across puzzles: # of boxes solved",
subtitle = "Grey lines are individual subjects, blue line and ribbon equal predicted mean + 95% CI") +
scale_x_continuous(limits = c(1, 8),
breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0, 300),
breaks = seq(0, 300, 60)) +
theme_minimal()
number of moves:
# null model: no learning over time
lm.moves_growth_null =
glmer(attempt_nInputEvents ~
1 +
# control vars
scale(astar_solution_length) +
scale(sokobanonline__solve_rate) +
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))# full model:
lm.moves_growth =
glmer(attempt_nInputEvents ~
1 +
trialNum +
# control vars
scale(astar_solution_length) +
scale(sokobanonline__solve_rate) +
(1 | puzzle_id_sorted) + # random slope for puzzle
(1 + trialNum | subject_id), # random slopes and intercepts per subject
data = df.analysis,
family = poisson(link = "log"),
control = glmerControl(optimizer = "bobyqa"))
lm.moves_growth %>%
summary()## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: poisson ( log )
## Formula:
## attempt_nInputEvents ~ 1 + trialNum + scale(astar_solution_length) +
## scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) +
## (1 + trialNum | subject_id)
## Data: df.analysis
## Control: glmerControl(optimizer = "bobyqa")
##
## AIC BIC logLik deviance df.resid
## 44553.5 44596.7 -22268.8 44537.5 1632
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -14.8471 -2.8981 -0.1796 2.5329 21.2837
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subject_id (Intercept) 0.278284 0.52753
## trialNum 0.007601 0.08718 -0.48
## puzzle_id_sorted (Intercept) 0.026888 0.16398
## Number of obs: 1640, groups: subject_id, 205; puzzle_id_sorted, 24
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 5.263749 0.050075 105.118
## trialNum -0.053067 0.006199 -8.561
## scale(astar_solution_length) 0.113277 0.034737 3.261
## scale(sokobanonline__solve_rate) -0.106784 0.034817 -3.067
## Pr(>|z|)
## (Intercept) < 2e-16 ***
## trialNum < 2e-16 ***
## scale(astar_solution_length) 0.00111 **
## scale(sokobanonline__solve_rate) 0.00216 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) trilNm sc(__)
## trialNum -0.363
## scl(str_s_) 0.004 -0.007
## scl(skb___) 0.002 -0.004 0.245## Data: df.analysis
## Models:
## lm.moves_growth_null: attempt_nInputEvents ~ 1 + scale(astar_solution_length) + scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## lm.moves_growth: attempt_nInputEvents ~ 1 + trialNum + scale(astar_solution_length) + scale(sokobanonline__solve_rate) + (1 | puzzle_id_sorted) + (1 + trialNum | subject_id)
## npar AIC BIC logLik deviance Chisq Df
## lm.moves_growth_null 7 44614 44652 -22300 44600
## lm.moves_growth 8 44554 44597 -22269 44538 62.87 1
## Pr(>Chisq)
## lm.moves_growth_null
## lm.moves_growth 2.209e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1df.analysis$predicted_moves =
predict(lm.moves_growth, type = "response")
df.analysis_subject =
df.analysis %>%
group_by(subject_id, trialNum) %>%
summarise(mean_pred = mean(predicted_moves, na.rm = TRUE),
.groups = "drop")
df.analysis_subject %>%
ggplot(aes(x = trialNum,
y = mean_pred)) +
geom_line(aes(group = subject_id),
alpha = 0.1, color = "gray") + # individual trajectories
stat_summary(fun = mean,
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun = "errorbar",
geom = "line",
size = 1,
color = "#1f77b4") + # average curve
stat_summary(fun.data = mean_cl_boot,
geom = "ribbon",
aes(group = 1),
fill = "#1f77b4",
alpha = 0.2) +
labs(x = "Puzzle #",
y = "# of moves",
title = "Predicted performance curves across puzzles: # of moves solved",
subtitle = "Grey lines are individual subjects, blue line and ribbon equal predicted mean + 95% CI") +
scale_x_continuous(limits = c(1, 8),
breaks = seq(1,8,1)) +
scale_y_continuous(limits = c(0, 600),
breaks = seq(0, 600, 100)) +
theme_minimal()